Nanoelectromechanical system (NEMS) resonators (generally denoted by the acronym NEMS for Nano Electro Mechanical System) are promising devices, particularly in the field of gas analysis.
The principle of detection of a species contained in a sample of said gas relies on the activation of a suspended beam of nanometer-scale dimensions at its resonant frequency, by way of an excitation signal (mechanical or electrical), and the detection of the displacement of said beam by means of at least one strain gauge.
The beam being functionalized by a given chemical substance, the passage of a sample of gas into a fluid channel wherein the resonator is placed enables the capture (for example by adsorption) by said substance of molecules of a species contained in the sample.
The capture of at least one molecule has the effect of modifying the resonant frequency of the beam, which is detectable in the output signal (generally electrical) of the strain gauge.
The resonator is connected to an electronic reading circuit, which firstly allows the beam to be activated into vibration by the excitation signal and secondly allows the output signal emitted by the strain gauge to be read.
Various structures of resonator have already been designed, comprising different types of beams (clamped-free, double-clamped etc.), different activation means (including thermoelastic, electrostatic activation means etc.) and a variety of detection techniques (including piezoresistive, piezoelectrical means etc.).
Such resonators can be fabricated on silicon substrates by means of the usual microelectronics techniques, including etching, deposition processes etc.
However, due to their nanometer-scale size, NEMS resonators are relatively fragile (particularly to mechanical and electrical impacts).
Moreover, their small surface area makes it difficult to capture species contained in very low concentrations in the samples to be analyzed.
To overcome these limitations, it can be advantageous to simultaneously use several resonators of this type, arranged in a network.
The expected advantages of a network of NEMS resonators are many.
Firstly, they offer a total surface area for capturing species for analysis which is larger if the number of beams is high.
This makes it possible to more accurately detect species contained in low concentrations in the gas sample to be analyzed.
Moreover, the use of a NEMS resonator network minimizes the impact of the failure of one of their number, which is compensated for by the operation of the other resonators of the network, thereby improving the robustness of the device.
Furthermore, for a network of N NEMS resonators, a detection limit gain in the order of √{square root over (N)} in terms of signal (or in the order of N in terms of power) could in theory be expected.
The detection limit can be estimated by calculating the Allan variance, which expresses the frequency measurement resolution (df/f ratio) as a function of the measurement time (also denoted by the term “integration time”).
The obtaining of such a gain of √{square root over (N)} can be denoted by the term “network effect”.
However, the production of a network of NEMS resonators comes up against various technological difficulties, in such a way that it has not been possible, to date, to fabricate a network allowing the expected network effect to be obtained.
Thus, the article by Bargatin et al. [Bargatin2012] describes a network of 2800 NEMS resonators connected in series and in parallel, wherein each resonator comprises a clamped-free silicon beam associated with a piezoresistive strain gauge composed of a metal layer deposited on the beam, the beam being thermoelastically activated in such a way as to vibrate out of the plane of the substrate in which it is fabricated.
The thermoelastic activation relies on the application to the resonators of an AC voltage at a frequency generating variations in the temperature of the beam at its resonant frequency.
To remove background noise, the authors employed differential measurement consisting in connecting two identical networks to the same input of the reading electronics, but applying a 180° phase shift to the signal sent to one of the networks with respect to the other, and by summing the output signals of each of the networks.
This article does however show disappointing results in terms of detection limit, particularly for long integration times, i.e. above 100 ms.
Thus, a detection limit comparable to that of an individual resonator was observed for integration times in the order of a few seconds.
According to the authors of the article, these results seem to be explained by problems of process variation in the resonance frequencies between resonators.
Specifically, the network effect cited above can only be obtained in ideal conditions, including in particular the hypothesis that the resonators of the network are perfectly identical to one another.
In practice, these conditions are difficult to achieve inasmuch as process variations, in particular, from one resonator to another are unavoidable.
[Bargatin 2012] thus indicates that the network used in the experiment exhibits variations in resonant frequency, which can be imputed to process variations, in the order of 1%.
As a result resonators with a response that is too different from that of the other resonators do not take part in the measurement, in such a way that, although the detection limit may be reduced, the network effect cannot be achieved.
The article by Mile et al. [Mile2010] presents an example of a different NEMS resonator from those used in [Bargatin2012].
This resonator comprises a clamped-free suspended beam, on either side of which extend two piezoresistive strain gauges made of doped silicon.
The activation of the beam is achieved electrostatically, by two electrodes set out on either side of the beam, leading to a vibration of the beam in the plane of the substrate in which is fabricated.
However, although this type of resonator, which has only been tested individually, appears promising in terms of signal-to-noise ratio, the measured Allan variance remains inexplicably higher than the theoretical variance due to an unknown form of noise, the nature of which has not been identified to date.
Now, the existence of this unidentified noise is likely to prevent the obtaining of a network effect if an attempt is made to combine said resonators in a network.
Indeed, if this noise is extrinsic to the resonators, or if it is intrinsic to the resonators but correlated from one resonator to another, a network effect cannot be obtained.
These phenomena must therefore be remedied to be able to produce a resonator network that effectively enables the desired network effect to be obtained.
Moreover, only collective addressing of the resonators is proposed in [Bargatin2012], i.e. all the resonators are connected to a single input and a single output, in such a way that it is not possible to read the output signal of each resonator.
In other words, the output signal of the network corresponds to the mean of the signals of the different resonators.
But it may be beneficial to address the resonators individually, i.e. to read the output signal of each resonator.
However, a NEMS resonator exhibits at least two, sometimes four interconnect pads for connecting with its reading electronics. Thus, for resonators of the type described in [Mile2010], when the activation mode and the detection mode are decoupled, i.e. different means are used, firstly for activating the beam and secondly for detecting its displacement, at least two pads are required for connecting the resonator to an activation circuit and at least two other pads are required for connecting to a detection circuit.
As a consequence, individual addressing of the resonators would suppose the multiplication of this number of interconnect pads by the number of resonators, which for a high number of resonators is technically impossible given the constraints relating to the overall size of the devices.
One aim of the invention is therefore to design a measurement system comprising NEMS resonators exhibiting improved performances in terms of detection limit and benefiting as much as possible from the expected network effect.
Another aim of the invention is to design a measurement system able to be fabricated according to a simple process that allows a system of small dimensions to be obtained.